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热门问题
在线解多元方程:
先设置方程的元(即未知数的个数),然后点击“下一步”按钮,即可输入方程组的各个元的系数,点击“下一步”按钮,即可获得方程组的解。
注意,方程组各元的系数只能是数字,不能是代数式(包括数学函数)。
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在线解多元方程
> 答案
详细信息:
输入的方程组为:
C
+
R
=
35
(1)
0 =
0
(2)
2
C
+
4
R
=
94
(3)
0 =
0
(4)
0 =
0
(5)
0 =
0
(6)
0 =
0
(7)
0 =
0
(8)
0 =
0
(9)
0 =
0
(10)
0 =
0
(11)
0 =
0
(12)
0 =
0
(13)
0 =
0
(14)
0 =
0
(15)
0 =
0
(16)
0 =
0
(17)
0 =
0
(18)
解题过程:
将第 (1) 等式两边 乘以2后,可以得到等式:
2
C
+
2
R
=
70
(19)
,然后再同时用第 (3) 等式两边 减去 等式(19)两边,方程组化为:
C
+
R
=
35
(1)
0 =
0
(2)
2
R
=
24
(3)
0 =
0
(4)
0 =
0
(5)
0 =
0
(6)
0 =
0
(7)
0 =
0
(8)
0 =
0
(9)
0 =
0
(10)
0 =
0
(11)
0 =
0
(12)
0 =
0
(13)
0 =
0
(14)
0 =
0
(15)
0 =
0
(16)
0 =
0
(17)
0 =
0
(18)
交换第(2)和第(3)式后,方程组化为:
C
+
R
=
35
(1)
2
R
=
24
(2)
0 =
0
(3)
0 =
0
(4)
0 =
0
(5)
0 =
0
(6)
0 =
0
(7)
0 =
0
(8)
0 =
0
(9)
0 =
0
(10)
0 =
0
(11)
0 =
0
(12)
0 =
0
(13)
0 =
0
(14)
0 =
0
(15)
0 =
0
(16)
0 =
0
(17)
0 =
0
(18)
将第 (2) 等式两边 除以2后,可以得到等式:
2
C
+
R
=
12
(20)
,然后再同时用第 (1) 等式两边 减去 等式(20)两边,方程组化为:
C
=
23
(1)
2
R
=
24
(2)
0 =
0
(3)
0 =
0
(4)
0 =
0
(5)
0 =
0
(6)
0 =
0
(7)
0 =
0
(8)
0 =
0
(9)
0 =
0
(10)
0 =
0
(11)
0 =
0
(12)
0 =
0
(13)
0 =
0
(14)
0 =
0
(15)
0 =
0
(16)
0 =
0
(17)
0 =
0
(18)
将未知数的系数化为1,方程组化为:
C
=
23
(1)
R
=
12
(2)
0 =
0
(3)
0 =
0
(4)
0 =
0
(5)
0 =
0
(6)
0 =
0
(7)
0 =
0
(8)
0 =
0
(9)
0 =
0
(10)
0 =
0
(11)
0 =
0
(12)
0 =
0
(13)
0 =
0
(14)
0 =
0
(15)
0 =
0
(16)
0 =
0
(17)
0 =
0
(18)
所以,方程组的解为:
C =
23
R =
12
其中: A, B, D, E, F, G, H, I, J, K, L, M, N, O, P, Q 为任意常数。
解方程组的详细方法请参阅:
《多元一次方程组的解法》
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